Imagemagick (and thus convert) doesn't seem to deal with the 16-bit colour (565) image format, so I wrote a program to expand the data to 24-bit (888) before passing it to convert. You can use mine (rgb565torgb888.py, 311 bytes) or any other one you may find out there. :)

Update: If you're using Python 3, here is a version which will work for you. Use it without redirection, like this: